Solve the system of equations and choose the correct ordered pair. 4x + 3y = 16
7x + 6y = 31

Answers

Answer 1

Answer:

The solution is, (1,4) is the solution of the system of equations and choose the correct ordered pair.

4x + 3y = 16

7x + 6y = 31

What is equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

equation: 1

4x+3y=16

y=(16-4x)/3

equation: 2

7x+6y=31

y=(31-7x)/6

now, we have,

(16-4x)/3 = (31-7x)/6

6(16-4x) = 3(31-7x)

96-24x=93-21x

3=3x

x=1

we get,

4x+3y=16, x=1

4(1)+3y=16

4+3y=16

3y=12

y=4

so, we have,

x=1, y=4

therefore the answer is B (1,4)

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Answer 2

Answer: 4x+3y=16 7x+6y=31
y=(16-4x)/3 y=(31-7x)/6
(16-4x)/3 = (31-7x)/6
6(16-4x) = 3(31-7x)
96-24x=93-21x
3=3x
x=1

4x+3y=16, x=1
4(1)+3y=16
4+3y=16
3y=12
y=4

x=1, y=4 therefore the answer is B (1,4)

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Given that cos (x) = 1/3, find sin (90 - x)

Answers

$sin((A - B)) \equiv sin(A)cos(B) - cos(A)sin(B) \n\n\therefore sin((90 - x))\n = sin((90))cos((x)) - cos((90))sin((x)) \n= (1)cos((x)) - (0)sin((x)) \n= cos(x) - 0 \n= cos(x) \n= (1)/(3)$

$90а= ( \pi )/(2) \n sin(90а-x)=sin (( \pi )/(2)-x)=cos (x) \n cos(x)= (1)/(3) \n sin(x)= (1)/(3) \approx0.33333 \n x=19а$

Solve for x and y: 3x+7y=22 12x+28y=88

Answers

Final answer:

The system of linear equations 3x + 7y = 22 and 12x + 28y = 88 actually represents the same line, indicating that there are infinite solutions. Any pair of (x, y) that satisfies one equation will satisfy the other.

Explanation:

To solve the system of linear equations 3x + 7y = 22 and 12x + 28y = 88, let's use substitution or elimination method. Here, the elimination method works best since the equations are multiples of each other. Divide the second equation by 4, you get 3x + 7y = 22, which is exactly the same equation as the first equation.

This means both equations represent the same line, so there are infinite solutions. Any x, y that satisfy one equation will satisfy the other. Therefore, the system is dependent.

Example of such solutions (x, y) can be obtained by isolating y in the first equation:

7y = 22 - 3x

y = (22 - 3x) / 7 or y = 9 + 3x

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Final answer:

The given system of equations has infinitely many solutions.

Explanation:

To solve for x and y in the given system of equations:

3x + 7y = 22

12x + 28y = 88

Multiply the first equation by 4 to eliminate the y variable:

12x + 28y = 88

Subtract the second equation from the first equation:

12x + 28y - 12x - 28y = 88 - 88

0 = 0

Since both variables have been eliminated, the equations are dependent and have infinitely many solutions. The solution is any pair of (x, y) values that satisfies the original equations.

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List all the factors of 22. 1, 2, 4, 6, 11, 22
1, 22
1, 2, 4, 11, 22
1, 2, 11, 22

Answers

1,4,22,11,1,2 those are the factors of 22 I hope i could help if u need them in order just tell me :)

Answer:

1,2,4,11,22

Step-by-step explanation:

Write 5.2 as the quotient of two integers A...11/3
B...21/5
C...26/5
D...51/10

Answers

Answer:

C) $(26)/(5) = 5.2$ .

Step-by-step explanation:

Given : Number 5.2

To find : write 5.2 as the quotient of two integers.

Solution : We have given Number 5.2

For $(11)/(3) = 3.666$ .

For $(21)/(5) = 4.2$ .

For $(26)/(5) = 5.2$ .

For $(51)/(10) = 5.1$ .

So, 5.2 is quotient of 26 and 5 integers.

Therefore, C) $(26)/(5) = 5.2$ .

it would be C because what i did A. 11 divided by 3=3.666666666666666666
B.21 divided by 5=4.2 C. 26 divided by 5= 5.2 D. 51 divided by 10=5.1 we want 5.2 and C = 5.2

Sam's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Sam $5.70 per pound, and type B coffee costs $4.15 per pound. This month, Sam made 142 pounds of the blend, for a total cost of $688.50. How many pounds of type B coffee did he use?

Answers

Answer:

165.90 pounds

Step-by-step explanation:

Answer:

165.90

Step-by-step explanation:

Using only five odd numbers, add them up so that the result is 32, the five odd numbers have to be whole numbers only.

Answers

This is not possible. If you add an odd number of odd numbers, you will get an odd number. If you add an even number of odd numbers, you will get an even number. 5 is an odd number, but 32 is an even number, so therefore it is not possible.

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Round 8.043 to the nearest hundredth

A group of Physicians must build an addition to their existing private clinic. They are considering three different sized additions; a small addition, a medium addition and a large addition. If the medical demand is high (there is a favorable market for the addition) they would realize a net profit of $100,000 with a large addition, a net profit of $40,000 with a medium addition and a net profit of $10,000 with a small addition. If the medical demand is low (there is an unfavorable market for the addition) they would realize a net loss of $40,000 with the large addition, a net loss of $10,000 with the medium addition and a net profit of $5,000 with the small addition. The Physicians were also able to assign the following utility preference values to each of the potential payoffs they could encounter. Utility of $100,000 is 1.0, U ($40,000) is 0.9, U ($10,000) is 0.6, U ($5,000) is 0.5, U ($-10,000) is 0.4, and U ($-40,000) is 0.0. The physicians also have a reliable forecast indicating a 40% probability of the high medical demand. Using expected monetary value theory, what should they do and what is the expected value of that decision? Using expected utility theory, what should they do and what is the expected utility of that decision?